The expression you provided is:

\[
\frac{5x + 3y}{9} - \frac{x - y}{3}
\]

To simplify this expression, follow these steps:

### Step 1: Find a common denominator.
The denominators are 9 and 3. The least common denominator (LCD) between them is 9. So, rewrite the second fraction with the denominator 9:

\[
\frac{5x + 3y}{9} - \frac{(x - y) \cdot 3}{3 \cdot 3} = \frac{5x + 3y}{9} - \frac{3(x - y)}{9}
\]

### Step 2: Combine the fractions.
Since both fractions now have the same denominator, combine them:

\[
\frac{5x + 3y - 3(x - y)}{9}
\]

### Step 3: Distribute and simplify.
Distribute the \(-3\) in the second term of the numerator:

\[
\frac{5x + 3y - 3x + 3y}{9}
\]

Combine like terms in the numerator:

\[
\frac{(5x - 3x) + (3y + 3y)}{9} = \frac{2x + 6y}{9}
\]

### Step 4: Factor out any common factors.
Factor out the common factor in the numerator:

\[
\frac{2(x + 3y)}{9}
\]

So, the simplified expression is:

\[
\frac{2(x + 3y)}{9}
\]

### Do you want further details or have any questions? 

Here are 5 related questions you might find interesting:
1. How do you find the least common denominator for different fractions?
2. What are some methods to simplify algebraic expressions?
3. Can you explain how to distribute and combine like terms?
4. How do you factor out common terms in an algebraic expression?
5. What are the steps to simplifying complex rational expressions?

**Tip:** Always check for common factors in the numerator and denominator; this can help simplify the expression more easily.

Learn how to simplify the algebraic expression (5x + 3y) / 9 - (x - y) / 3 step by step. This problem involves finding the least common denominator and applying the distributive property. Suitable for students in Grades 8-10.

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